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lfunc_lfunctions • Show schema
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{'Lhash': '324921360187705392269298615490', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 3.0], 'a4': [0, 0], 'a5': [-11.104686356149273, 1.2984378812835757], 'a6': [0, 0], 'a7': [0, -16.209372712298546], 'a8': [0, 0], 'a9': [-9.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.64183360551102, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, -3.0]]], [5, [[1.0, 0], [11.104686356149273, -1.2984378812835757]]]], 'bad_primes': [2, 3, 5], 'central_character': '960.769', 'coefficient_field': 'CDF', 'conductor': 960, 'conductor_radical': 30, 'conjugate': '1027474418858563560189312446698', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -3.0]], [[1.0, 0], [11.104686356149273, -1.2984378812835757]], [[1.0, 0], [0, 16.209372712298546], [-343.0, 0]], [[1.0, 0], [40.209372712298546, 0], [1331.0, 0]], [[1.0, 0], [0, 19.790627287701454], [-2197.0, 0]], [[1.0, 0], [0, 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0.14287467558609618], 'positive_zeros': ['0.25631775832331570205085822254417', '1.80484286687918247020763659405589', '2.89842614835947036478143944501972', '3.97110719126549774277080327935498', '5.16172532638493311697288665766366', '5.91794218707413854285266948417028', '7.04579010513617666373750870874148', '7.78516268670009788251395143883173', '8.468444708679054963411658983035362', '9.163300974027634675921210679797827'], 'prelabel': '2-960-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.526076906696543, 'root_angle': -0.5370507857072188, 'root_number': '-0.1161358146844350822648592357509548817033744146709329872 - 0.9932333424465685710509264939859010961542477717541164730*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2685253928536094', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.25631775832331570205085822254', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 56.64183360551102, 'bad_primes': [2, 3, 5], 'central_character': '5.4', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/960/4/f/p/769/3'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-960-5.4-c3-0-11', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-960-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.526076906696543, 'root_angle': -0.2685253928536094, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.25631775832331570205085822254', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '324921360187705392269298615490', 'Lhash_array': ['324921360187705392269298615490'], 'label': '2-960-5.4-c3-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/4/f/p/769/3'}